Australia's replies came from Sam Kerr, Caitlin Foord and Emily Gielnik in the seven-goal feast at Ibaraki Kashima Stadium.
It was 36-year-old Rapinoe and 39-year-old Lloyd who stole the show, though, on what may prove to be farewell appearances for the superstar duo.
Whether they play on in the short term for the national team remains to be seen, but this was likely a final outing at the Olympics for both, and they went out in style.
Rapinoe opened the scoring in the eighth minute when her wicked in-swinging corner from the left evaded everybody and found the net.
Kerr levelled seven minutes later with her 48th goal for Australia – a new national team record – when her shot proved too powerful for Adrianna Franch, but it was soon Rapinoe's time again.
The standout player from the 2019 World Cup smashed in her second goal of this game on the volley, connecting sweetly from around 12 yards after Alanna Kennedy sliced an attempted clearance.
Lloyd, who became the outright second most-capped player in US history by making her 312th appearance, got in on the goals just before half time. Her thumping left-footed shot across goal found the right corner, putting the US 3-1 up.
Lloyd scored again in the 51st minute after another Kennedy error, this time a weak header back to her goalkeeper allowing Lloyd a clear run on goal, with the striker slotting home.
That made her the US team's all-time highest scorer in Olympic women's football with 10 goals. Lloyd won Olympic gold in 2008 and 2012, with Rapinoe also on the triumphant latter team in London.
Australia got back into this game with a header from Foord after 54 minutes, and Kerr headed against the left post two minutes later. Substitute Gielnik rattled in a delicious late third for Australia, but they could not find a fourth.
Bird, 40, signed off her Games career in the United States' 90-75 win over Japan on Sunday.
At courtside was Rapinoe, who won a bronze on Thursday when she scored twice as the USA beat Australia 4-3 in the football third-place match.
Rapinoe, who won the Golden Boot and Golden Ball at the 2019 World Cup, first met Bird in the run-up to the 2016 Rio Olympics.
They became a couple later that year and announced their engagement in October 2020.
When the USA clinched the basketball gold medal, Bird went to the side of the court and kissed Rapinoe, later revealing how her 36-year-old partner managed to gain access to the Saitama Super Arena.
"I'm very lucky," Bird said. "Obviously when your partner or your fiancee is also in the Olympics you would love to be able to go and support them, be around them, to give any kind of support possible.
"Megan somehow finagled a media credential and got herself in this arena today. We didn't really know it was going to happen until two days ago, it got confirmed. So I do I feel very lucky she was here to witness it, to share it with me."
Spectators have been blocked from attending venues at the Olympics due to the COVID-19 pandemic, with families of overseas athletes unable to travel to Japan for the Games, meaning Rapinoe was among the fortunate few to be in the arena.
"I just went over and obviously told her I loved her and told her I was tired," said Bird. "That was pretty much the extent of the conversation, and she told me she was happy and proud of me.
"Of course I'm so proud of her and her team for winning that bronze medal. The Olympics is hard. It's really hard. There's so much pressure involved and so to have both of us medal is something that I know we'll take that memory with us forever."
Rapinoe wrote on Instagram: "I am so proud of you @sbird10. As if I could love you any more. Congrats baby!"
Bird has ruled out playing on to Paris 2024, happy to settle for five gold medals, the first of which came in Athens at the 2004 Games.
"It really is hard to wrap your head around it, to grasp what it is," said the Seattle Storm star.
"Twenty years of staying true to the game, making sure you're at the top of your game, so much sacrifice.
"The only thing about getting older, you know all the bad stuff that can happen. We lost in 2006 [to Russia at the World Championship]. We tasted that and that's always been the driver.
"So when we actually have the medal around our necks, it just feels so good. It's a sense of relief in a lot of ways."
USA had 17 attempts on Monday but a second defeat at the Games – they had gone down 3-0 to Sweden in their opening group fixture – means the reigning world champions will not have a chance to secure gold in Japan.
There was controversy surrounding the winning goal, too, as a VAR check resulted in Canada being awarded a penalty for a foul by Tierna Davidson on Deanne Rose in the 74th minute.
Substitute goalkeeper Adrianna Franch, who had replaced the injured Alyssa Naeher in the first half, guessed correctly but Fleming's penalty still found the net.
Canada stubbornly held on for the remainder of the contest to secure a first triumph over their rivals since March 11, 2001.
While USA can still claim a bronze medal, Megan Rapinoe did not hold back when assessing the impact of the result, particularly against opponents they have become accustomed to beating through the years.
"It's a bitter one to swallow. We never want to lose to Canada. I don't think I ever have, so it's a bitter one," Rapinoe said.
"Still a lot to compete for. It's not the colour we wanted, but there's still a medal on the line and that's a huge thing. We want to win that game, but this sucks. It sucks."
Asked why USA had struggled so much to find form during the tournament, Rapinoe replied: "I feel like we haven't had our joy a little bit.
"It just hasn't flowed for us, hasn't been easy. It's not for a lack of effort, or anyone not giving everything they have. It just didn't click for us.
"I don't know if it was roster rotation, I know it's a tough tournament when trying to save people, but our bench is as deep as hell. I don't think we can put it on that, and I can't quite put my finger on it.
"We just didn't have that juice that we normally do."
USA had been aiming to strike Olympic gold for a fifth time having missed out on a medal of any colour at Rio 2016, where they lost to Sweden on penalties in the last eight.
The Swedes lost to Germany in the final five years ago but could still go one better this year – they take on Australia in the second semi-final.
Strikes either side of the half-time whistle from Stina Blackstenius and a goal by Lina Hurtig proved the difference as Sweden claimed a famous triumph over their heavyweight rivals, who they defeated on penalties in the 2016 quarter-finals.
The world champions enjoyed a two-year spell without losing before the Group G opener but will quickly have to bounce back if they are to follow up their France 2019 success with Olympic gold.
Rapinoe found it hard to defend the USA's performance as she credited Sweden's hard-working display.
"We did not play a very good game and that is to take nothing away from Sweden, they played a great game," the attacking midfielder said after the match.
"This is the highest level and these are the best teams in the world. Sweden are one of the best ever in Europe and the world. If we don't play well we don’t win these games.
"We want to be a lot better, we played a bit tight and hurt ourselves a lot. You can't say one thing specifically.
"I can't remember the last time we gave up a goal, so to give up three is not great but we know what we need to do to win these games, get out of the group and go from there."
Head coach Vlatko Andonovski refused to panic and is keen to see a response against New Zealand on Saturday.
"It has put us in a big hole and we are the only ones who can get ourselves out of it," he said. "It is not going to be easy. We have to get good results in the next two games, but I know this team will not give up.
"I don’t remember this team losing 3-0 in recent history so it is a bit of a shock, but everyone is positive. We still have games ahead of us. We have got to bounce back. We have to forget this game and focus on the next one."
In contrast, Blackstenius, whose brace sealed a remarkable victory, spoke glowingly of her team, who were without Chelsea captain Magdalena Eriksson for the win.
"I'm very happy about the goals - of course I'm happy to score. The team helped me very much and I think I could have scored at least two more but I don't want to focus on that. I'm just happy and proud of the team", the forward said.
“We developed our game and our play. It's very good and we have so much quality in every player. Every player is also very different from the other. We have so many players that can do good stuff and as a team we are very good. Every player is very happy about going very attacking."
Hedvig Lindahl, though, maintained that Sweden's win was simply a starting point and that Peter Gerhardsson's side had not achieved what they had come to the Games for yet.
"It's just the first group game, we haven't won anything yet. We need to keep going," the veteran goalkeeper said. "If you have one high into lows in the group then this means nothing. But to win against the USA, it's something we can take some confidence from.
"You can go very far in a tournament even if you lose to the USA or whoever you play in the first game, so I don't know how much it means, but we showed the world and ourselves that we can play good against a team like the US and any team."
